What are the divisors of 4533?

1, 3, 1511, 4533

There is a total of 4 positive divisors.
The sum of these divisors is 6048.
The arithmetic mean is 1512.

4 odd divisors

1, 3, 1511, 4533

How to compute the divisors of 4533?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 4533 by each of the numbers from 1 to 4533 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

4533 / 1 = 4533 (the remainder is 0, so 1 is a divisor of 4533)
4533 / 2 = 2266.5 (the remainder is 1, so 2 is not a divisor of 4533)
4533 / 3 = 1511 (the remainder is 0, so 3 is a divisor of 4533)
...
4533 / 4532 = 1.0002206531333 (the remainder is 1, so 4532 is not a divisor of 4533)
4533 / 4533 = 1 (the remainder is 0, so 4533 is a divisor of 4533)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 4533 (i.e. 67.327557508052). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

4533 / 1 = 4533 (the remainder is 0, so 1 and 4533 are divisors of 4533)
4533 / 2 = 2266.5 (the remainder is 1, so 2 is not a divisor of 4533)
4533 / 3 = 1511 (the remainder is 0, so 3 and 1511 are divisors of 4533)
...
4533 / 66 = 68.681818181818 (the remainder is 45, so 66 is not a divisor of 4533)
4533 / 67 = 67.65671641791 (the remainder is 44, so 67 is not a divisor of 4533)